Most learning to rank research has assumed that the utility of different documents is independent, which results in learned ranking functions that return redundant results. The few approaches that avoid this have rather unsatisfyingly lacked theoretical foundations, or do not scale. We present a learning-torank formulation that optimizes the fraction of satisfied users, with a scalable algorith...

Suppose f(x, y) is a binary form of degree d with coefficients in a field K ⊆ C. The K-rank of f is the smallest number of d-th powers of linear forms over K of which f is a K-linear combination. We prove that for d ≥ 5, there always exists a form of degree d with at least three different ranks over various fields. The K-rank of a form f (such as x3y2) may depend on whether -1 is a sum of two s...

The use of phrases in retrieval models has been proven to be helpful in the literature, but no particular research addresses the problem of discriminating phrases that are likely to degrade the retrieval performance from the ones that do not. In this paper, we present a retrieval framework that utilizes both words and phrases flexibly, followed by a general learning-to-rank method for learning ...

We consider the extension of the last-in-first-out graph searching game of Giannopoulou and Thilikos to digraphs. We show that all common variations of the game require the same number of searchers, and the minimal number of searchers required is one more than the cycle-rank of the digraph. We also obtain a tight duality theorem, giving a precise min-max characterization of obstructions for cyc...

We revisit a geometric lower bound for Waring rank of polynomials (symmetric rank of symmetric tensors) of [LT10] and generalize it to a lower bound for rank with respect to arbitrary varieties, improving the bound given by the “non-Abelian” catalecticants recently introduced by Landsberg and Ottaviani. This is applied to give lower bounds for ranks of multihomogeneous polynomials (partially sy...

We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p) and points of a nondegenerate Hermitian variety. As a corollary, we obtain new bounds for the size of caps and the existence of ovoids in finite unitary spaces. This paper is a companion to [2], in which Blokhuis and this author derive the analogous p-ranks for quadrics.

We describe how we build the system for NTCIR-13 Short Text Conversation (STC) Chinese subtask. In our system, we use the retrieval-based method and the generationbased method respectively. For the retrieval-based method, we develop several features to match the candidates and then apply a learning to rank algorithm to get properly ranked results. For the generation-based method, we first gener...

It is an open problem to find a good characterization for independence or, more generally, the rank function in the d-dimensional rigidity matroid of a graph when d ≥ 3. In this paper we give a brief survey of existing lower and upper bounds on the rank of the 3-dimensional rigidity matroid of a graph and introduce a new upper bound, which may lead to the desired good characterization.

A fuzzy-nets based in-process adaptive surface roughness control (FNASRC) system was developed in this research. The FNASRC system was able to adapt cutting parameters in-process and in a real time fashion to improve the surface roughness of machined parts when the surface roughness quality was not meeting customer requirements in the end milling operations. The FNASRC system was comprised of t...

An event chronicle provides people with an easy and fast access to learn the past. In this paper, we propose the first novel approach to automatically generate a topically relevant event chronicle during a certain period given a reference chronicle during another period. Our approach consists of two core components – a timeaware hierarchical Bayesian model for event detection, and a learning-to...